[MBDyn-users] Eigenanalysis : compute deformed shape

Romuald NORET romuald.noret at cdr.hutchinson.fr
Thu Dec 3 12:05:50 CET 2009


Hello,

Thanks, I almost understood but I have a two last questions :
Each line of VR (right eignevectors)  matrix are all degree of freedom of 
the analysis :
- It is a displacement or a position? I believe it is a position, but I 
would like to be sure.
- Each column is a degree of freedom, with real and imaginray part, for 
instance : "(...) 0.0000000000000000e+00 0.0000000000000000e+00 
0.0000000000000000e+00  1.2489399063226966e-11-i*  1.1826429422174239e-03 
(...)"
In this example,
"1.2489399063226966e-11-i*  1.1826429422174239e-03" means : Re(dof_i+1) 
="1.2489399063226966e-11" and Im(dof_i+1)="1.1826429422174239e-03"
But how interpret this value :"0.0000000000000000e+00" means : Re(dof_i) 
="0" and Im(dof_i)="0" ?
Thank you in advance.

Best regards,
Romuald Noret




Pierangelo Masarati <masarati at aero.polimi.it> 
02/12/2009 15:08

A
Romuald NORET <romuald.noret at cdr.hutchinson.fr>
cc
mbdyn-users at mbdyn.org
Objet
Re: [MBDyn-users]  Eigenanalysis : compute deformed shape






Romuald NORET wrote:

> I am tried to convert m out file to vmo file to watch modal shape into 
> easyanim. I understood well how to write this vmo file, but I still have 
a 
> problem :
> I remember you already explained how right and left eigenvectors are 
> computed, but I failed into understanding how to compute deformed shape. 
I 
> apologize if I lose the part of documentation about it, but can I ask 
how 
> to do it?

I'm not familiar with the vmo format; as far as I recall it's very 
simple.  You need to use the right eigenvectors (VR).

The contents of that matrix is: each column is an eigenvector.  They 
contain perturbations of node position and orientation.  Position 
perturbations are in the units you used for node positions; orientation 
perturbations technically are perturbations of Cayley-Gibbs-Rodrigues 
parameters; you can think of them as the usual linear rotations of FEM, 
in radians.  Position and rotation perturbations are oriented according 
to the global reference frame.

What "matters" is what is contained in each row.  It is not 
straightforward.  In order to help, the .log file contains a string, 
something like

struct node dofs: 0 6 18

the numbers listed above represent the offset of the rows related to 
each structural node, in the order of the "structural node:" rows in the 
same file.  I'm reporting a simple example below, taken from a model 
where 3 nodes, labeled 1, 2, 3, are connected by a single beam element,

output frequency: 1
structural node: 1 0 0 0 euler123 -0 0 0
structural node: 2 0.5 0 0 euler123 -0 0 0
structural node: 3 1 0 0 euler123 -0 0 0
clamp: 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1
beam3: 1 1 0 0 0 2 0 0 0 3 0 0 0
struct node dofs: 0 6 18
   real mm2in = 0.0393701
   ...

So the position and orientation perturbations of each node can be 
determined using the offsets illustrated above.  In the above example, 
the positions of node labeled "1" are VR(0 + 1:3, :), the rotations are 
VR(0 + 4:6, :); the positions of node labeled "2" are VR(6 + 1:3, :), 
the rotations are VR(6 + 4:6, :); and so on.

Hope this helps.

Cheers, p.

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